1.Ages of College Students The dean of students wants to see whether there is a significant difference in ages of resident students and commuting students. She selects a sample of 30 students from each group. The ages are shown here. At =0.01, decide if there is enough evidence to reject the claim of no difference in the ages of the two groups. Use the standard deviations from the samples and the P-value method; use 1 for the average age of resident students. Assume =14.1 and =25 (rounded to one decimal place).

Resident students

27 26 18 19 18 30

26 18 18 19 32 23

19 19 18 29 19 22

18 22 26 19 19 21

23 18 20 18 22 21

Commuter students

28 25 20 24 26 30

22 22 22 21 18 20

19 26 35 19 19 18

19 32 29 23 21 19

36 27 27 20 20 21

(b) Compute the test value. Round the sample means to at least one decimal place and final answer to two decimal places.

z=?

(c) Find the P-value.

p=?

2.At age 9, the average weight 21.3kg and the average height 124.5cm for both boys and girls are exactly the same. A random sample of 9-year-olds yielded these results.

Boys Girls

Sample size 50 50

Mean height, cm 123.5 121.7

Population variance 98 120

Estimate the mean difference in height between boys and girls with 95% confidence. Round your intermediate calculations to two decimal places and final answers to one decimal place.

? < 1- 2 < ?

3.Home Prices A real estate agent compares the selling prices of homes in two municipalities in a certain location to see if there is a difference. The results of the study are shown. Is there enough evidence to reject the claim that the average cost of a home in both locations is the same? Use =0.01.

City A City B

=X1$97,750 =X2$99,000

=1$5602 =2$4731

=n137 =n239

(b) Find the critical value(s). Round the answer(s) to at least two decimal places. If there is more than one critical value, separate them with commas.

Critical value(s):?

(c) Compute the test value.

Using the formula for the z test for comparing two means from independent populations, compute the test value: ?

4.Professional Golfers' Earnings Two random samples of earnings of professional golfers were selected. One sample was taken from the Professional Golfers Association, and the other was taken from the Ladies Professional Golfers Association. At =0.05, is there a difference in the means? The data are in thousands of dollars. Use the critical value method with tables.

PGA

446 1147 1344 5687 10,508

4910 8553 7573 375

LPGA

48 466 863 100 1876

2029 4364 2921

Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.

Critical value(s):?

(c)Compute the test value.

t=?

5.Weights of Vacuum Cleaners Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a sample of each type. At =0.01, can it be concluded that the means of the weights are different? Assume the variables are normally distributed and the variances are unequal.

Hard body types Soft body types

21 17 13 20 24 18 24 13

15 16 18 18 11 13 12

23 17 17 16

17 15

Use 1 for the mean weight of the hard body type.

Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.

Critical value(s):?

(c)Compute the test value.

t=?

6.Retention Test Scores A sample of non-English majors at a selected college was used in a study to see if the student retained more from reading a 19th-century novel or by watching it in DVD form. Each student was assigned one novel to read and a different one to watch, and then they were given a 100-point written quiz on each novel. Assume the variables are normally distributed. The test results are shown below.

Book 88 73 91 85 93 95 90 90 80 90

DVD 80 95 95 92 93 80 92 75 70 80

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At =0.10, can it be concluded that the book scores are higher than the DVD scores?

(b) Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.

Critical value(s):?

c) Compute the test value.

t=?

7.Cholesterol Levels A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At =0.10, did the cholesterol level decrease on average? Use the critical value method and tables.

Patient 1 2 3 4 5 6

Before 238 218 216 223 208 221

After 215 201 193 191 203 213

(b) Find the critical value(s). Round the answer to at least three decimal places. If there is more than one critical value,

separate them with commas.

Critical value(s):?

(c) Compute the test value.

t=?

8.PGA Golf Scores At a recent PGA tournament (the Honda Classic at Palm Beach Gardens, Florida) the following scores were posted for eight randomly selected golfers for two consecutive days. At =0.10, is there evidence of a difference in mean scores for the two days? Assume the variables are normally or approximately normally distributed and use D for the mean on Thursday minus the mean on Friday.

Golfer 1 2 3 4 5 6 7 8

Thursday 65 67 65 70 68 68 68 70

Friday 67 68 70 70 69 71 72 69

(b) Find the critical value(s). Round the answer(s) to three decimal places. If there is more than one critical value, separate them with commas.

Critical value(s):?

(c) Compute the test value.

t=?

9.Smoking Survey National statistics show that 23% of men smoke and 18.5% of women do. A random sample of 134 men indicated that 29 were smokers, and of 96 women surveyed, 9 indicated that they smoked.

Construct a 95% confidence interval for the true difference in proportions of male and female smokers. Use p1 for the proportion of men who smoke. Round your answers to three decimal places.

?< p1- p2

10.Victims of Violence A random survey of 75 women who were victims of violence found that 22 were attacked by relatives. A random survey of 53 men found that 14 were attacked by relatives. At =0.05, can it be shown that the percentage of women who were attacked by relatives is greater than the percentage of men who were attacked by relatives? Use p1 for the proportion of women who were attacked by relatives. Use the critical value method with tables and round all intermediate calculations to at least three decimal places.

(b)Find the critical value(s). Round the answers to two decimal places.

Critical value(s):?

(c)Compute the test value.

t=?